This paper considers a hybrid two-stage flow-shop scheduling problem with m identical parallel machineson one stage and a batch processor on the other stage.The processing time of job Jj on any of m identical parallel machines is aj≡a(j∈N),and the processing time of job Jj is bj(j∈N)on a batch processor M.We take makespan(Cmax)as our minimization objective.In this paper,for the problem of FSMP-BI(m identical parallel machines on the first stage and a batch processor on the second stage),based on the algorithm given by Sung and Choung for the problem of l I rj,BI I Cmax under the constraint of the given processing sequence,we develop an optimal dynamic programming Algorithm H1 for it in max{O(nlogn),O(nB)} time.A max{O(nlogn),O(nB)} time symmetric Algorithm H2 is given then for the problem of BI-FSMP(a batch processor on the first stage and m identical parallel machines on the second stage).